A leak on reddit claims the download for the beta is 12.63GB and will offer 4 story missions, a strike, 4 PvP maps and a larger area than the alpha to explore.
Also bungie released a statement saying that people should expect there to be hiccups in the beta. Even though the alpha went well and smooth they are going to "kick the servers" and make sure they can still function. They are saying that this isn't just so you can try before you buy, but they are doing actual testing and using us as the lab rats. So if things get weird, they are trying to make things break so they can prepare for the full launch.